The present invention is at least generally related to flywheel energy storage systems and, more particularly, to embodiments of an advanced flywheel hub and associated method.
A flywheel may be regarded as a mechanical device, having a significant moment of inertia, that may be used as a storage device for rotational energy. For example, flywheels resist changes in their rotational speed such that an energy input or an energy output is required in order to change the rotational speed of a given rotating flywheel. In predominantly mechanical systems, such as an automobile engine, this requirement may cause the flywheel to exert a stabilizing influence on the system. The same holds for electro-mechanical systems. For example, an electrical motor may include a flywheel for resisting sudden changes in rotational speed of the motor.
In recent decades, high speed flywheels have been employed in electro-mechanical systems that may be configured as electrical storage devices such that the devices can be electrically charged and discharged in a manner that is at least generally analogous to the charging and discharging of conventional rechargeable batteries. In this context, a flywheel can be “charged”, for storing energy by using electrical energy provided, for example, through electrical cables to increase the speed of the flywheel to cause an increase in the rotational energy. The flywheel can be subsequently discharged by decreasing the speed to cause a decrease in the rotational energy of the flywheel while converting this rotational energy into electrical energy for delivery, for example through electrical cables, from the flywheel to some external load.
An electrical machine can be attached to a flywheel rotor assembly, for example, using a single shaft, and configured for operating in one of several modes including but not limited to (i) a charging mode with the electrical machine operating as a motor for receiving electrical energy and for increasing the rotational speed of the flywheel, and (ii) a discharging mode with the electrical machine operating as a generator for providing electrical energy via a decrease in the speed of the flywheel and (iii) a float mode with the electrical machine spinning freely without adding or subtracting rotational energy to or from the wheel. It is noted that in the float mode a given flywheel may exhibit residual power losses, for example due to frictional losses, that may cause at least gradual decreases in stored rotational energy even if no electrical power is entering or leaving the flywheel through the electrical machine. For purposes of descriptive clarity, and based on well known conventions, it is noted that an electrical machine attached to a flywheel and configured for operation in one or more of these three modes may be referred to hereinafter as a motor.
It will be readily appreciated by a person of ordinary skill in the art that a maximum energy storage capacity of a flywheel system may depend on a maximum rotational speed at which the flywheel rotor assembly can be rotated, without delaminating or otherwise failing as a result of internal stresses for example due to centrifugal forces, and that an increase in the maximum speed causes a corresponding increase in the maximum storage capacity in proportion to the square of the maximum speed. For example, as will be described hereinafter, the maximum speed of a given flywheel rotor assembly may be determined as the speed at which centrifugal forces cause separation between separate parts of the flywheel rotor assembly. In another example, the maximum speed of a flywheel rotor may be limited by the stiffness of the given flywheel rotor assembly.
It will be further appreciated that the maximum rotational speed can be sufficiently high that the presence of any ambient gas at atmospheric pressure can cause severe power loss and overheating that can result in catastrophic failures. For example, flywheel systems described throughout this disclosure may operate at rotational speeds well above 10,000 rpm. In some applications, a vacuum pressure of less than 10 mTorr is required in order to avoid excessive power loss and rotor heating. In view of these considerations and based on well known techniques, it is often necessary to contain a flywheel in a housing that at least provides an airtight seal for supporting low pressure vacuum surrounding the flywheel rotor.
Turning now to the figures, FIG. 1 is a diagrammatic elevational view, in cross-section, illustrating one example of a prior art electro-mechanical flywheel unit, generally indicated by the reference number 100, that can be utilized for storing rotational energy as part of an electrical energy storage system. Flywheel unit 100 includes a flywheel rotor assembly, generally indicated by reference number 105 having a rotatable shaft 110 that supports a rim 115 using a hub 120 for rotation as indicated by an arrow 122 in a selected direction which can be either clockwise or counterclockwise. The flywheel unit of the present example may be contained in an airtight sealed housing 125 that at least supports low vacuum therein and that provides at least some degree of containment in the event of a high speed failure such as delamination of the rim. Furthermore, flywheel housing 125 may be configured to provide structural support for a number of components therein, as will be described immediately hereinafter.
Flywheel unit 100 includes an electrical motor 126, shown within a dashed rectangle, having a motor rotor assembly 135 that is connected with shaft 110 for co-rotation with the shaft, and a motor stator assembly 140 that is supported by housing 125 through a support structure 145, as needed.
Based on well known techniques, the flywheel rotor may be radially constrained using a lower bearing assembly 150 and an upper bearing assembly 150′. The bearing assemblies can be supported by lower and upper mechanical damper assemblies 155 and 155′, respectively, that are connected to housing 125 through support structure 145.
In accordance with well known principles of mechanics, the maximum storage capacity of flywheel unit 100 may depend in part on a moment of inertia the rotor such that a rotor having a higher moment of inertia, with a given maximum speed, may exhibit a proportionally higher storage capacity as compared to a rotor with a lower moment of inertia. Furthermore, it will be appreciated that bearing assemblies capable of operating at high maximum rotational speeds, for example above 15,000 rpm, may be incapable, at least when operating at such high speeds, of withstanding axial forces of more than just a few pounds. In this regard, it is often desirable to configure a given flywheel unit with a flywheel levitation apparatus for limiting axial forces on the bearings by supporting at least a majority of the weight of the rotor in the axial direction using a flywheel levitation apparatus.
Rim 115 may be configured with an inside diameter DRIM and the rim may exhibit a predetermined radial rim stiffness as a resistance to radial expansion, at least with respect to inside diameter DRIM, responsive to centrifugal forces caused by operational rotation of the flywheel rotor assembly. Hub 120 may be configured for supporting the rim by engaging the inside diameter thereof such that an outside diameter DHUB expands sufficiently for maintaining contact between the hub and the rim, at least up to and including a maximum speed beyond which the contact between the hub and the rim becomes so tenuous that the hub fails in at least one of (i) supporting the rim, and (ii) transmitting torque between the shaft and the hub. It will be appreciated by a person of ordinary skill in the art, familiar with high speed flywheel energy storage systems, that maintaining engagement, between a flywheel rim and its associated hub, can be highly challenging. Applicants recognize that in many applications, resistance to hub-rim separation is a controlling factor in determining the maximum rotational speed for a given flywheel rotor assembly.
With respect to assembly of a flywheel rotor, it will be appreciated by a person of ordinary skill in the art that at least some amount of rotor imbalance is inevitable, even for precision-balanced flywheel rotor assemblies that have been manufactured according to state-of-the art high precision assembly and/or balancing techniques. For example, a flywheel rotor assembly weighing several hundred pounds, having been assembled based on state-of-the art high precision techniques, may nevertheless exhibit ten gram-inches of imbalance. This imbalance could be caused by a number of well-known phenomena including but not limited to (i) deviations from roundness (out of roundness) wherein a rotationally symmetric component, such as the shaft, exhibits some deviation from roundness, (ii) fluctuations in mass density associated with a given rotor component, such as the rim, and (iii) some degree of misalignment in a given fitting between two rotor components. It is noted that ten gram-inches may be interpreted, according to well known terms of art, as being at least approximately equivalent to the presence of a 1 gram weight at a radial displacement of ten inches from an axis of rotation of the rotor assembly.
Based on standard practice, the imbalance of a given flywheel rotor assembly may be characterized using a precision balancing system, after assembly and prior to installation in a flywheel system, and any measured imbalance may be corrected based on well known balancing techniques. However, it is noted that even utilizing state-of-the art precision balancing, in conjunction with well established rotor balancing techniques, some residual imbalance may remain after assembly and/or during operation. Furthermore, deformations during high speed operation may cause unpredictable imbalances to emerge, for example as dynamic imbalances due to slightly non-uniform rim expansion, despite substantial removal thereof prior to operation.
Based on well known principles of rotor-dynamics, any imbalance in a given flywheel rotor assembly may give rise to upper and lower imbalance forces 164′ and 164″ that may be exerted by the rotor, through one or both of the bearings, and on the bearing dampers, such that the imbalance force oscillates synchronously with the spinning of the rotor and has a frequency that is equal to a rotational frequency of the flywheel rotor assembly. While reference numbers designated with prime marks are used herein for distinguishing between the upper and lower imbalance forces, reference number 164 may be used hereinafter to refer to imbalance forces collectively in a general sense. It is noted that the upper and lower imbalance forces may be the same or different from one another.
Imbalance forces 164 may cause some degree of transverse motion that may be limited in part by the dampers. It will be appreciated by a person of ordinary skill in the art that in some applications the dampers may be configured to provide an amount of damping that is particularly configured for limiting motion radial motion due to imbalance forces 164. It will be further appreciated by a person of ordinary skill in the art, familiar with rotor dynamics, that unacceptably large radial motions, particularly at very high rotational frequencies above several thousand revolutions per minute (RPM) may lead to complex rotor dynamic motion that may de difficult to characterize and control. For example, for a flywheel rotor weighing several hundred pounds, radial motion substantially exceeding twenty or thirty mils may result in some degree of cross-coupling of rotational energy from the intended rotation of the flywheel about an axis of rotation 163 into undesired twisting motion about a transverse axis of inertia 166 that is oriented cross-wise to axis of rotation 163. One low-speed (and correspondingly low frequency) example of an analogous form of rotor-dynamic cross-coupling may be familiar to anybody who has grasped a fast-spinning bicycle wheel while attempting to twist the axis about a transverse axis thereof. This well known demonstration provides at least some conceptual framework for appreciating how transverse motion of a rotor can, at least in some cases, lead to substantial transverse forces thereon. Insofar as a bicycle wheel is a relatively low speed rotor of relatively light weight, it can be readily appreciated that a heavy rotor (hundreds of pounds) spinning orders of magnitude faster (tens of thousands of RPM) may be susceptible to analogous forces of comparatively extreme magnitude, even in the event of relatively small twisting motions about any transverse axis thereof. At least in light of these considerations, it can be appreciated that for heavy rotors (hundreds or thousands of pounds) rotating at speeds of over 10,000 rpm, limiting the extent of any substantial transverse motions may be required, at least for generally avoiding cross-coupling forces of such severe strength as to be potentially destructive to the flywheel rotor.
It will be yet further appreciated by a person of ordinary skill in the art, familiar with rotor dynamics, that no flywheel rotor can be infinitely rigid with respect to flexure, and that forces due to imbalance may cause vibration of the flywheel rotor, especially in cases where the rotational frequency of operation matches a mechanical resonance of the flywheel rotor. In the latter case, radial forces 164 may cause the rotor to periodically vibrate, in a bending mode, at the frequency of rotation of the flywheel rotor assembly, much as a metal rod may vibrate when struck by a hammer. Vibration of the rotor may cause transverse vibrational motion of at least a portion of the rotor. These transverse vibrational motions may in turn lead to cross-coupling of energy into an inertial axis, such as axis 166, that is not aligned with axis of rotation 163. As described above, even relatively small transverse motions may lead to undesired forces of substantial magnitude, and therefore are to be avoided. Therefore, limiting the extent of rotor vibrations may be required, at least for generally avoiding cross-coupling forces of such severe strength as to be potentially destructive to the flywheel rotor. Furthermore, due to nuances of rotor dynamics, Applicants appreciate that it is often necessary to limit any flexure of the rotor, in the bending mode, to amplitudes that are substantially smaller as compared to acceptable limitations that may be associated with transverse motion of the bearing as dampers.
Attention is now turned to FIG. 2, which is a diagrammatic elevational view, of a flywheel rotor assembly 105, illustrating a fundamental bending mode thereof. Dashed lines 168 indicate an unflexed shape of the rotor prior to any flexure, and solid lines depict the flywheel rotor assembly flexing in a fundamental bending mode. The flexure may take approximately the shape illustrated in FIG. 2, and may have an amplitude 170′ at an upper end of the rotor, and an amplitude 170″ at a lower end. It is noted that amplitudes 170′ and 170″ may be the same or different from one another, depending on a number of factors including but not limited to symmetry or asymmetry of the rotor with respect to upper and lower halves thereof, and a distribution of imbalances throughout the rotor. It is considered by Applicants that the relevant descriptions herein at least generally hold with respect to both cases. While reference numbers designated with prime marks have been used to distinguish between the upper and lower amplitudes, reference number 170 may be used hereinafter to refer collectively and in a general sense to the amplitudes of bending modes. It is further noted that the amplitudes are shown as highly exaggerated in the figure for purposes of illustrative clarity.
For any mechanical structure and/or assembly, as will be appreciated by one versed in the theory of mechanical vibration, such a structure may exhibit a plurality of bending modes, any selected one of which may be characterized in part as having an associated bending mode frequency, as a frequency at which the selected mode vibrates. One or more modes in the plurality may have a bending mode frequency that is equal to or lower than the bending mode frequency associated with all the other bending modes. In accordance with standardized nomenclature, the lowest frequency may be referred to as the fundamental frequency such that any mode that tends to vibrate at the fundamental frequency is referred to as the fundamental mode. The mechanical structure may exhibit additional bending modes, of successively higher order and having successively higher bending mode frequencies. In accordance with well established nomenclature, the fundamental bending mode may be interchangeably referred to as a first order mode, and the next successively higher frequency mode may be referred to as a second order mode (not shown in FIG. 2), and so on for additional higher order modes. When these bending modes are regarded as resonant modes, in accordance with well established theories of vibrations, each mode may receive energy from some applied force, such that the amplitude of vibration (for example amplitude 170 in FIG. 2) grows as the received energy increases.
As described above, a rotor imbalance can give rise to radial forces 164. Based on well known principles of mechanics, and in accordance with Newton's third law, this radial force may produce an equal and opposite force (not shown), by the bearing on the rotor. This force is one variety of forces that may cause the flywheel rotor assembly to flex in a motion that can be characterized as some combination of vibrations associated with various ones of the plurality of bending modes, including any fundamental bending mode. Any coupling of energy into each bending mode, for example due to oscillating external and/or internal forces, may depend on the frequency at which the applied force oscillates. In particular, as will be described immediately hereinafter, the fundamental bending mode may exhibit a strong tendency to receive energy from any external forces that are applied to the flywheel rotor at approximately the fundamental bending mode frequency. As the rotational speed slows, the frequency of the applied force correspondingly decreases, and coupling of energy into the fundamental bending mode will generally decrease exponentially. It will be appreciated by a person of ordinary skill in the art that for speeds at which the angular frequency is substantially lower than the fundamental bending mode frequency, any amount of energy coupled into the fundamental bending mode may be sufficiently limited such that amplitude 170 is sufficiently limited. Negative consequences associated with any flexure, in this mode, can be avoided in this way. On the other hand, for high speed operational speeds at which the rotational frequency of the flywheel rotor assembly matches the fundamental bending mode frequency of the flywheel rotor, at least to an approximation, the flywheel rotor may resonantly couple substantial amounts of energy into the fundamental bending mode. Based on complex, yet well established, principles of rotor dynamics, even a relatively small amplitude 170 (for example several mils), of flexure of the rotor, can lead to substantial cross-coupling of energy into rotor axes of inertia (such as axis 166) that are not aligned with the axis of rotation 163. The rotor-dynamics resulting from such transfers of energy can be complex and/or highly unstable, so that the onset of this form of instability can occur rapidly (within a few rotations of the rotor) and may produce destructive forces on and/or within the rotor assembly. At least for this reason, in many applications it is widely held that operation at or near the frequency of the fundamental bending mode frequency is to be completely avoided. At least for these reasons, a given flywheel rotor, having a maximum speed of rotation as described above, may be configured to exhibit a fundamental bending mode having a frequency that substantially exceeds the rotational frequency of the maximum speed of the rotor. For example, one may routinely adhere to a design goal specifying that for a given rotor the fundamental bending mode frequency should exceed the maximum rotational frequency by a substantial margin.
For purposes of enhancing the reader's understanding, coupling of energy into the fundamental bending mode due to radial forces 164 has initially been described. However, it is to be appreciated that energy coupling is not limited in this regard, and that energy may be coupled, from the flywheel rotor assembly, into the fundamental bending mode by a variety of mechanisms. As one well known example, based on well established terms of art, the fundamental bending mode may receive energy in the manner of a self-excited vibration, wherein the energy may couple through complex combinations of mechanisms. Irrespective of the particular manner in which the fundamental mode may receive rotational energy from the flywheel, at least for the reasons described above, Applicants appreciate that it is often advantageous to avoid operation at or near the fundamental bending mode frequency of a given flywheel rotor assembly, at least for a wide variety of rotor assembly configurations.
The foregoing examples of the related art and limitations related therewith are intended to be illustrative and not exclusive. Other limitations of the related art will become apparent to those of skill in the art upon a reading of the specification and a study of the drawings.